A freight train has a mass of 1.5 × 107 kg.

If the locomotive can exert a constant pull
of 4.9×105 N, how long does it take to increase
the speed of the train from rest to 74 km/h?
Answer in units of min.

F=ma

a=F/m

vf=at
t= vf/a=vf*m/Force

change vf to m/s, and you have it.

To calculate the time it takes to increase the speed of the train from rest to 74 km/h, we can use Newton's second law:

F = m * a

Where:
F is the force applied by the locomotive (4.9×10^5 N),
m is the mass of the train (1.5 × 10^7 kg),
a is the acceleration of the train (to be determined),
v is the final velocity of the train (74 km/h).

First, let's convert the final velocity from km/h to m/s:
74 km/h = (74 * 1000) m/3600 s = 20556.889 m/s

Next, we can use the formula:
a = F/m

Substituting the known values:
a = (4.9×10^5 N) / (1.5 × 10^7 kg) = 0.0327 m/s² (rounded to four decimal places)

Now, we can use the equation of motion:
v = u + at

Where:
v is the final velocity (20556.889 m/s),
u is the initial velocity (0 m/s),
a is the acceleration (0.0327 m/s²),
t is the time (to be determined).

Rearranging the equation, we get:
t = (v - u) / a

Substituting the values:
t = (20556.889 m/s - 0 m/s) / 0.0327 m/s²
t = 628195.1282 s

Finally, we can convert the time from seconds to minutes:
t = (628195.1282 s) / (60 s/min) ≈ 10469.919 min

Therefore, it takes approximately 10469.919 minutes to increase the speed of the train from rest to 74 km/h.

To find the time it takes to increase the speed of the train, we need to use the equation of motion:

F = ma

Where:
- F is the force applied by the locomotive (4.9 × 10^5 N),
- m is the mass of the train (1.5 × 10^7 kg),
- a is the acceleration, and
- we can assume the train starts from rest, so the initial velocity (v0) is 0.

We can rearrange the equation to solve for the acceleration:

a = F/m

Substituting the given values:

a = (4.9 × 10^5 N) / (1.5 × 10^7 kg)
= 0.0327 m/s²

To find the time it takes to increase the speed, we need to find the distance traveled. We can use the equation:

v = u + at

Where:
- v is the final velocity (74 km/h),
- u is the initial velocity (0 m/s),
- a is the acceleration (0.0327 m/s²), and
- t is the time we want to find.

First, we need to convert the final velocity from km/h to m/s:

v = 74 km/h × (1000 m/1 km) × (1 h/3600 s)
= 20.56 m/s

Rearranging the equation, we get:

t = (v - u) / a

Substituting the known values:

t = (20.56 m/s - 0 m/s) / 0.0327 m/s²
≈ 628.35 s

To convert the time from seconds to minutes, we divide by 60:

t = 628.35 s / 60
≈ 10.47 min

Therefore, it takes approximately 10.47 minutes to increase the speed of the train from rest to 74 km/h.